A Kalman filter algorithm can be used to perform optimum estimation on a state of a linear white Gaussian noise system, and is widely used in GNSS positioning and navigation. For the Kalman filter algorithm, a state equation is first utilized to predict states of a receiver, for example, a current position, speed, and clock error, then pseudorange and Doppler shift values of each satellite are predicted according to estimated state values and satellite positions and speeds provided by a satellite ephemeris, and finally a corrected optimum estimated value is obtained by processing measured residuals. After a new measured value is obtained each time, the Kalman filter algorithm may be used to update an estimated state value of the system once, and becomes an effective method for improving real-time GNSS navigation and positioning.
In a conventional Kalman filter positioning method, auxiliary devices such as a sensor and a barometer and a Kalman filter algorithm having a heading constraint and a speed constraint are usually used to improve the positioning accuracy of a height of a GNSS. In these methods, a peripheral is used, or information such as a heading and a real-time speed needs to be known. Consequently, costs of satellite positioning are increased.